reserve X for set;
reserve CS for non empty CollStr;
reserve a,b,c for Point of CS;
reserve CLSP for CollSp;
reserve a,b,c,d,p,q,r for Point of CLSP;
reserve i,j,k for Element of NAT;
reserve CLSP for proper CollSp;
reserve a,b,c,p,q,r for Point of CLSP;
reserve P,Q for LINE of CLSP;

theorem
  a<>b implies Line(a,b) <> the carrier of CLSP
proof
  assume a<>b;
  then ex r st not a,b,r are_collinear by Th12;
  hence thesis by Th11;
end;
